Simplify the following expression: $x = \dfrac{10q^2 + 150q + 500}{q + 5} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $10$ , so we can rewrite the expression: $ x =\dfrac{10(q^2 + 15q + 50)}{q + 5} $ Then we factor the remaining polynomial: $q^2 + {15}q + {50} $ ${5} + {10} = {15}$ ${5} \times {10} = {50}$ $ (q + {5}) (q + {10}) $ This gives us a factored expression: $\dfrac{10(q + {5}) (q + {10})}{q + 5}$ We can divide the numerator and denominator by $(q - 5)$ on condition that $q \neq -5$ Therefore $x = 10(q + 10); q \neq -5$